#include "towns.h"
#include<bits/stdc++.h>
using namespace std;
int f1, f2;
map<pair<int,int>,int> res;
int getDist(int a, int b){
if (a == b) return 0;
if (a > b) swap(a, b);
if (res.find({a, b}) == res.end()) res[{a, b}] = getDistance(a, b);
return res[{a, b}];
}
int eq(int a, int b){
return getDist(f1, a)+getDist(f1, b)-getDist(a, b);
}
int hubDistance(int N, int sub){
res.clear();
int bsf = 0;
for (int i=1; i<N; i++){
int d = getDist(0, i);
if (d > bsf){
bsf = d;
f1 = i;
}
}
bsf = 0;
for (int i=0; i<N; i++){
if (i == f1) continue;
int d = getDist(f1, i);
if (d > bsf){
bsf = d;
f2 = i;
}
}
int diam = getDist(f1, f2);
map<int,vector<int>> m;
int R = pow(10, 9);
for (int i=0; i<N; i++){
int jp = (getDist(f1, 0)+getDist(f1, i)-getDist(0, i))/2;
m[jp].push_back(i);
R = min(R, max(jp, diam-jp));
}
int xl = 0, xm, xr = N;
bool bal = false;
for (auto [jp, v] : m){
xr -= v.size();
xm = v.size();
if ((jp == R || diam-jp == R) && xl <= N/2 && xr <= N/2){
if (xm <= N/2) bal = true;
else {
vector<bool> in(N, false);
for (int x : v) in[x] = true;
vector<int> l, b;
for (int i=0; i<N; i++){
if (l.empty()) l.push_back(i);
else {
if (in[i] && in[l.back()] && eq(i, l.back()) != 2*jp) b.push_back(i);
else {
l.push_back(i);
if (!b.empty()){
l.push_back(b.back());
b.pop_back();
}
}
}
}
int t = l.back();
while (!l.empty()){
if (in[t] && in[l.back()] && eq(t, l.back()) != 2*jp){
if (l.size() == 1){
b.push_back(l.back());
l.pop_back();
}
else {
l.pop_back();
l.pop_back();
}
}
else {
l.pop_back();
if (b.empty()) break;
b.pop_back();
}
}
if (b.empty()) bal = true;
}
}
xl += v.size();
}
if (bal) return R;
else return -R;
}
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